—Calibration of the spatial sensitivity functions of coil arrays is a crucial element in parallel magnetic resonance imaging (pMRI). The self-calibrating technique for sensitivity extraction has complemented the common calibration technique that uses a separate pre-scan. In order to improve the accuracy of sensitivity estimate from small number of self-calibrating data, which is extracted from a fully sampled central region of a variable-density k-space acquisition in self-calibrating parallel images, a novel scheme for estimating the sensitivity profiles is proposed in the paper. On consideration of truncation error and measurement errors in self-calibrating data, the issue of calculating sensitivity would be formulated as a regularized least squares estimation problem, which is solved by the preconditioned conjugate gradients algorithm. When applying the estimated coil sensitivity to reconstruct full field-of-view(FOV) image from the under-sampling simulated and in vivo data, the normalized signal-to-noise ratio (NSNR) of reconstruction image is evidently improved, and meanwhile the normalized mean squared error (NMSE) is remarkably reduced, especially when a rather large accelerate factor is used.
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